(2x+5)(4x+2)=0

Solution for (2x+5)(4x+2)=0 equation:

(2x+5)(4x+2)=0

We multiply parentheses ..

(+8x^2+4x+20x+10)=0

We get rid of parentheses

8x^2+4x+20x+10=0

We add all the numbers together, and all the variables

8x^2+24x+10=0

a = 8; b = 24; c = +10;
Δ = b2-4ac
Δ = 242-4·8·10
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16}{2*8}=\frac{-40}{16}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16}{2*8}=\frac{-8}{16}
=-1/2
$